TMZ published an audio recording of a phone call between Cousins and Christy West, his ex-girlfriend and the mother of his 7-year-old son. Cousins, from Mobile, asked her if their son would be allowed to attend his wedding.
He allegedly threatened to "put a bullet through (her) f---ing head" after she said no.
Cousins married Morgan Lang this past weekend in Atlanta.
West is said to have recorded the call and provided police with a copy.
"We are aware of the allegation involving DeMarcus Cousins and, of course, take this claim seriously," the Lakers said in a statement. "We are in the process of gathering information and will reserve further comment at this time."
A defense attorney interviewed by USA Today said it's unlikely the four-time NBA All-Star would face jail time.
Cousins missed most of last season with the Golden State Warriors as he recovered from an Achilles tendon tear sustained in January 2018.
He signed a one-year deal with the Lakers in July but tore a knee ligament during a workout earlier this month. He could miss the entire season with his new team after knee surgery.